Problem

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. perpendicular to $4 y=x-4$ and passes through the point $(-2,1)$

Solution

Step 1 :Find the slope of the given line. The slope of the line \(4y = x - 4\) is \(\frac{1}{4}\).

Step 2 :The slope of a line perpendicular to this line is the negative reciprocal of \(\frac{1}{4}\), which is \(-4\).

Step 3 :Use the point-slope formula to find the equation of the line. The point-slope formula is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line. In this case, \((x_1, y_1) = (-2, 1)\) and \(m = -4\).

Step 4 :Rearrange the equation to the slope-intercept form, which is \(y = mx + b\).

Step 5 :The equation of the line in slope-intercept form is \(\boxed{y = -4x - 7}\).

From Solvely APP
Source: https://solvelyapp.com/problems/45901/

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